OAI/NumberTheory/Ostmann/Preliminaries/FiniteCauchyEstimate.lean

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Coefficient bounds by finite Fourier inversion on a circle

For a finite polynomial, a sufficiently large root-of-unity grid recovers every coefficient exactly. This supplies the Cauchy estimate used in Section 5.3, including for finite-dimensional operator spaces, without a dimension factor.

  1. def OAI.Ostmann.cyclicPolynomial line 15
  2. theorem OAI.Ostmann.cyclicPolynomial_eq_invDFT line 20
  3. theorem OAI.Ostmann.cyclicPolynomial_coefficient line 28
  4. theorem OAI.Ostmann.normalized_dft_norm_le line 35
  5. theorem OAI.Ostmann.cyclicPolynomial_coefficient_norm_le line 52
  6. theorem OAI.Ostmann.cyclicPolynomial_two_coefficient_norm_le line 62